Subgroups — C₈×#121×C₁₂₇ #44585158

Order 32512.

1222 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₂₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₁₂₇	C₂	1	1	yes	maximal, characteristic
5	C₁₂₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₂₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₂₇×#1923	C₂	1	2	yes	maximal, complemented
8	C₁₂₇×#1869	C₂	1	2	yes	maximal, complemented
9	C₁₂₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₄⋊C₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₁₂₇	C₂	1	2	yes	maximal, complemented
12	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₂₇	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
15	C₂×#121×C₁₂₇	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₂₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
19	C₈×D₄×C₁₂₇	—	2	8	no	—
20	C₈×D₄×C₁₂₇	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₁₂₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₁₂₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₂₇	—	2	4	no	—
29	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₂₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
34	#390×C₁₂₇	C₄	1	1	yes	characteristic
35	#389×C₁₂₇	C₄	1	1	yes	characteristic
36	#388×C₁₂₇	C₄	1	2	yes	—
37	#386×C₁₂₇	C₄	1	2	yes	—
38	#380×C₁₂₇	C₄	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₁₂₇	C₂²	1	2	yes	—
41	#336×C₁₂₇	C₂²	1	2	yes	—
42	#336×C₁₂₇	C₂²	1	2	yes	—
43	#336×C₁₂₇	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₂₇	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₂₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₂₇	—	2	2	no	—
51	C₂²×C₈×C₁₂₇	—	2	2	no	—
52	C₂²×C₈×C₁₂₇	—	2	2	no	—
53	C₂²×C₈×C₁₂₇	—	2	2	no	—
54	C₂²×C₈×C₁₂₇	—	2	2	no	—
55	C₂²×C₈×C₁₂₇	—	2	4	no	—
56	C₂²×C₈×C₁₂₇	—	2	4	no	—
57	C₂²×C₈×C₁₂₇	—	2	4	no	—
58	C₂²×C₈×C₁₂₇	D₄	1	4	yes	complemented
59	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₂₇	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
65	#121×C₁₂₇	C₈	1	8	yes	direct product factor
66	C₄×D₄×C₁₂₇	—	2	4	no	—
67	C₄×D₄×C₁₂₇	—	2	4	no	—
68	C₄×D₄×C₁₂₇	—	2	2	no	—
69	C₄×D₄×C₁₂₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₂₇	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₁₂₇	—	2	2	no	—
80	C₂×C₄²×C₁₂₇	—	2	2	no	—
81	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₂₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₁₂₇	—	2	4	no	—
87	C₄⋊C₈×C₁₂₇	—	2	2	no	—
88	C₄⋊C₈×C₁₂₇	—	2	2	no	—
89	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
90	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
91	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
92	C₂²⋊C₈×C₁₂₇	—	2	4	no	—
93	C₄×C₈×C₁₂₇	—	2	2	no	—
94	C₄×C₈×C₁₂₇	—	2	2	no	—
95	C₄×C₈×C₁₂₇	—	2	4	no	—
96	C₄×C₈×C₁₂₇	—	2	2	no	—
97	C₄×C₈×C₁₂₇	D₄	1	4	yes	complemented
98	#95×C₁₂₇	C₂×C₄	1	2	yes	—
99	#95×C₁₂₇	C₂×C₄	1	2	yes	—
100	#95×C₁₂₇	C₂×C₄	1	2	yes	—
101	C₂⁴×C₁₂₇	C₂²×C₄	1	2	yes	—
102	C₂⁴×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×D₄×C₁₂₇	—	2	4	no	—
104	C₂×D₄×C₁₂₇	—	2	4	no	—
105	C₂×D₄×C₁₂₇	—	2	2	no	—
106	C₂×D₄×C₁₂₇	—	2	2	no	—
107	C₂×D₄×C₁₂₇	C₂×C₈	1	8	yes	complemented
108	C₂×D₄×C₁₂₇	C₂×C₈	1	4	yes	complemented
109	C₂²×C₄×C₁₂₇	—	2	2	no	—
110	C₂²×C₄×C₁₂₇	—	2	2	no	—
111	C₂²×C₄×C₁₂₇	—	2	2	no	—
112	C₂²×C₄×C₁₂₇	—	2	2	no	—
113	C₂²×C₄×C₁₂₇	—	2	2	no	—
114	C₂²×C₄×C₁₂₇	—	2	1	no	—
115	C₂²×C₄×C₁₂₇	—	2	1	no	—
116	C₂²×C₄×C₁₂₇	—	2	1	no	—
117	C₂²×C₄×C₁₂₇	—	2	1	no	—
118	C₂²×C₄×C₁₂₇	—	2	2	no	—
119	C₂²×C₄×C₁₂₇	—	2	2	no	—
120	C₂²×C₄×C₁₂₇	—	2	2	no	—
121	C₂²×C₄×C₁₂₇	—	2	2	no	—
122	C₂²×C₄×C₁₂₇	—	2	2	no	—
123	C₂²×C₄×C₁₂₇	—	2	2	no	—
124	C₂²×C₄×C₁₂₇	C₂×C₈	1	4	yes	complemented
125	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₂₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₂₇	#41	1	2	yes	—
135	C₂²×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₂₇	—	2	8	no	—
137	C₂×C₈×C₁₂₇	—	2	1	no	—
138	C₂×C₈×C₁₂₇	—	2	1	no	—
139	C₂×C₈×C₁₂₇	—	2	1	no	—
140	C₂×C₈×C₁₂₇	—	2	1	no	—
141	C₂×C₈×C₁₂₇	—	2	1	no	—
142	C₂×C₈×C₁₂₇	—	2	1	no	—
143	C₂×C₈×C₁₂₇	—	2	8	no	—
144	C₂×C₈×C₁₂₇	—	2	2	no	—
145	C₂×C₈×C₁₂₇	—	2	2	no	—
146	C₂×C₈×C₁₂₇	—	2	2	no	—
147	C₂×C₈×C₁₂₇	—	2	2	no	—
148	C₂×C₈×C₁₂₇	—	2	2	no	—
149	C₂×C₈×C₁₂₇	—	2	2	no	—
150	C₂×C₈×C₁₂₇	—	4	8	no	—
151	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₂₇	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₁₂₇	#41	1	2	yes	—
156	C₂×C₈×C₁₂₇	#41	1	2	yes	—
157	C₄⋊C₄×C₁₂₇	—	2	4	no	—
158	C₄⋊C₄×C₁₂₇	—	2	2	no	—
159	C₄⋊C₄×C₁₂₇	—	2	2	no	—
160	C₄⋊C₄×C₁₂₇	C₂×C₈	1	4	yes	complemented
161	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
162	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
163	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
164	C₂²⋊C₄×C₁₂₇	—	2	4	no	—
165	C₂²⋊C₄×C₁₂₇	C₂×C₈	1	8	yes	complemented
166	C₄²×C₁₂₇	—	2	2	no	—
167	C₄²×C₁₂₇	—	2	2	no	—
168	C₄²×C₁₂₇	—	2	1	no	—
169	C₄²×C₁₂₇	—	2	2	no	—
170	C₄²×C₁₂₇	—	2	1	no	—
171	C₄²×C₁₂₇	—	2	2	no	—
172	C₄²×C₁₂₇	C₂×D₄	1	2	yes	—
173	C₄²×C₁₂₇	#41	1	2	yes	—
174	C₂³×C₁₂₇	—	2	1	no	—
175	C₂³×C₁₂₇	—	2	1	no	—
176	C₂³×C₁₂₇	—	2	1	no	—
177	C₂³×C₁₂₇	—	2	1	no	—
178	C₂³×C₁₂₇	—	2	2	no	—
179	C₂³×C₁₂₇	—	2	2	no	—
180	C₂³×C₁₂₇	—	2	2	no	—
181	C₂³×C₁₂₇	—	2	2	no	—
182	C₂³×C₁₂₇	—	2	2	no	—
183	C₂³×C₁₂₇	—	2	2	no	—
184	C₂³×C₁₂₇	C₄×D₄	1	2	yes	—
185	C₂³×C₁₂₇	C₂²×C₈	1	4	yes	—
186	C₂³×C₁₂₇	C₂²×C₈	1	2	yes	—
187	C₂³×C₁₂₇	#131	1	2	yes	—
188	C₂³×C₁₂₇	C₂³×C₄	1	1	yes	characteristic
189	D₄×C₁₂₇	—	2	16	no	—
190	D₄×C₁₂₇	—	2	8	no	—
191	C₂×C₄×C₁₂₇	—	2	8	no	—
192	C₂×C₄×C₁₂₇	—	2	1	no	—
193	C₂×C₄×C₁₂₇	—	2	1	no	—
194	C₂×C₄×C₁₂₇	—	2	1	no	—
195	C₂×C₄×C₁₂₇	—	2	2	no	—
196	C₂×C₄×C₁₂₇	—	2	1	no	—
197	C₂×C₄×C₁₂₇	—	2	1	no	—
198	C₂×C₄×C₁₂₇	—	2	1	no	—
199	C₂×C₄×C₁₂₇	—	2	1	no	—
200	C₂×C₄×C₁₂₇	—	2	1	no	—
201	C₂×C₄×C₁₂₇	—	2	2	no	—
202	C₂×C₄×C₁₂₇	—	2	2	no	—
203	C₂×C₄×C₁₂₇	—	2	2	no	—
204	C₂×C₄×C₁₂₇	—	2	2	no	—
205	C₂×C₄×C₁₂₇	—	2	2	no	—
206	C₂×C₄×C₁₂₇	—	2	8	no	—
207	C₂×C₄×C₁₂₇	—	2	2	no	—
208	C₂×C₄×C₁₂₇	—	2	2	no	—
209	C₂×C₄×C₁₂₇	—	2	2	no	—
210	C₂×C₄×C₁₂₇	—	2	2	no	—
211	C₂×C₄×C₁₂₇	—	2	2	no	—
212	C₂×C₄×C₁₂₇	—	2	2	no	—
213	C₂×C₄×C₁₂₇	—	4	2	no	—
214	C₂×C₄×C₁₂₇	—	4	2	no	—
215	C₂×C₄×C₁₂₇	—	4	2	no	—
216	C₂×C₄×C₁₂₇	—	4	2	no	—
217	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
219	C₂×C₄×C₁₂₇	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₁₂₇	C₂²×C₈	1	2	yes	—
221	C₂×C₄×C₁₂₇	C₂²×C₈	1	4	yes	—
222	C₂×C₄×C₁₂₇	C₂²×C₈	1	2	yes	—
223	C₂×C₄×C₁₂₇	#131	1	2	yes	—
224	C₂×C₄×C₁₂₇	#131	1	2	yes	—
225	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₂₇	C₂×#41	1	1	yes	characteristic
231	C₈×C₁₂₇	—	2	2	no	—
232	C₈×C₁₂₇	—	2	2	no	—
233	C₈×C₁₂₇	—	2	2	no	—
234	C₈×C₁₂₇	—	4	2	no	—
235	C₈×C₁₂₇	—	4	2	no	—
236	C₈×C₁₂₇	#121	1	4	yes	direct product factor
237	C₂²×C₁₂₇	—	2	2	no	—
238	C₂²×C₁₂₇	—	2	2	no	—
239	C₂²×C₁₂₇	—	2	2	no	—
240	C₂²×C₁₂₇	—	2	2	no	—
241	C₂²×C₁₂₇	—	2	2	no	—
242	C₂²×C₁₂₇	—	2	2	no	—
243	C₂²×C₁₂₇	—	2	4	no	—
244	C₂²×C₁₂₇	—	2	4	no	—
245	C₂²×C₁₂₇	—	2	4	no	—
246	C₂²×C₁₂₇	—	4	2	no	—
247	C₂²×C₁₂₇	—	4	2	no	—
248	C₂²×C₁₂₇	—	4	2	no	—
249	C₂²×C₁₂₇	—	4	2	no	—
250	C₂²×C₁₂₇	C₈×D₄	1	4	yes	complemented
251	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₁₂₇	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₁₂₇	C₄×#41	1	1	yes	characteristic
254	C₂²×C₁₂₇	C₂³×C₈	1	1	yes	characteristic
255	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
256	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
257	C₂²×C₁₂₇	C₂×#131	1	1	yes	characteristic
258	C₄×C₁₂₇	—	2	2	no	—
259	C₄×C₁₂₇	—	2	4	no	—
260	C₄×C₁₂₇	—	2	2	no	—
261	C₄×C₁₂₇	—	2	2	no	—
262	C₄×C₁₂₇	—	2	2	no	—
263	C₄×C₁₂₇	—	4	2	no	—
264	C₄×C₁₂₇	—	4	2	no	—
265	C₄×C₁₂₇	C₈×D₄	1	4	yes	complemented
266	C₄×C₁₂₇	C₂×#121	1	1	yes	characteristic
267	C₄×C₁₂₇	#525	1	1	yes	characteristic
268	C₄×C₁₂₇	#529	1	1	yes	characteristic
269	C₄×C₁₂₇	#532	1	1	yes	characteristic
270	C₈×#121	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂×C₁₂₇	—	2	4	no	—
272	C₂×C₁₂₇	—	4	4	no	—
273	C₂×C₁₂₇	C₄×#121	1	1	yes	characteristic
274	C₂×C₁₂₇	C₂×C₈×D₄	1	1	yes	characteristic
275	C₂×C₁₂₇	C₂×C₈×D₄	1	1	yes	characteristic
276	C₂×C₁₂₇	#2929	1	1	yes	characteristic
277	C₂×C₁₂₇	#2931	1	1	yes	characteristic
278	C₂×C₁₂₇	C₈×#41	1	1	yes	characteristic
279	C₂×C₁₂₇	#2966	1	1	yes	characteristic
280	C₂×C₈×D₄	C₂×C₁₂₇	1	2	yes	complemented
281	C₂×C₈×D₄	C₂×C₁₂₇	1	1	yes	characteristic, complemented
282	C₂²×C₄×C₈	C₂×C₁₂₇	1	1	yes	characteristic, complemented
283	C₄×#121	C₂×C₁₂₇	1	1	yes	characteristic
284	#1954	C₂×C₁₂₇	1	1	yes	characteristic, complemented
285	#1939	C₂×C₁₂₇	1	1	yes	characteristic, complemented
286	#1923	C₂×C₁₂₇	1	2	yes	complemented
287	#1869	C₂×C₁₂₇	1	2	yes	complemented
288	#1797	C₂×C₁₂₇	1	1	yes	characteristic, complemented
289	C₈×C₄⋊C₄	C₂×C₁₂₇	1	1	yes	characteristic, complemented
290	C₈×C₂²⋊C₄	C₂×C₁₂₇	1	2	yes	complemented
291	C₁₂₇	C₈×#121	1	1	yes	characteristic, direct product factor, Sylow
292	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
293	C₂³×C₈	C₂²×C₁₂₇	1	2	yes	—
294	C₂³×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
295	C₂×#121	C₄×C₁₂₇	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂²×C₁₂₇	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₁₂₇	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
299	C₈×D₄	—	2	8	no	—
300	C₈×D₄	—	2	4	no	—
301	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₁₂₇	1	2	yes	—
304	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
306	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
307	C₂×C₂²⋊C₈	C₂²×C₁₂₇	1	2	yes	—
308	C₂×C₄×C₈	—	2	4	no	—
309	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂²×C₁₂₇	1	2	yes	—
313	C₂×C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
314	#390	C₄×C₁₂₇	1	1	yes	characteristic
315	#389	C₄×C₁₂₇	1	1	yes	characteristic
316	#388	C₄×C₁₂₇	1	2	yes	—
317	#386	C₄×C₁₂₇	1	2	yes	—
318	#380	C₄×C₁₂₇	1	1	yes	characteristic
319	C₄×C₄⋊C₄	C₂²×C₁₂₇	1	1	yes	characteristic
320	C₄×C₂²⋊C₄	C₂²×C₁₂₇	1	2	yes	—
321	#336	C₂²×C₁₂₇	1	2	yes	—
322	#336	C₂²×C₁₂₇	1	2	yes	—
323	#336	C₂²×C₁₂₇	1	2	yes	—
324	C₂²×D₄	C₂×C₄×C₁₂₇	1	2	yes	—
325	C₂²×D₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
326	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
327	C₂³×C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₁₂₇	1	2	yes	—
329	C₂³×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	2	2	no	—
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	—	2	4	no	—
336	C₂²×C₈	—	2	4	no	—
337	C₂²×C₈	—	2	4	no	—
338	C₂²×C₈	D₄×C₁₂₇	1	4	yes	complemented
339	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
340	C₂²×C₈	C₂³×C₁₂₇	1	2	yes	—
341	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₂₇	1	1	yes	characteristic
345	#121	C₈×C₁₂₇	1	8	yes	direct product factor
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₁₂₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂×C₄×C₁₂₇	1	2	yes	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
362	C₂×C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₁₂₇	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
366	C₄⋊C₈	—	2	4	no	—
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₂²⋊C₈	—	2	4	no	—
370	C₂²⋊C₈	—	2	4	no	—
371	C₂²⋊C₈	—	2	4	no	—
372	C₂²⋊C₈	—	2	4	no	—
373	C₄×C₈	—	2	2	no	—
374	C₄×C₈	—	2	2	no	—
375	C₄×C₈	—	2	4	no	—
376	C₄×C₈	—	2	2	no	—
377	C₄×C₈	D₄×C₁₂₇	1	4	yes	complemented
378	#95	C₂×C₄×C₁₂₇	1	2	yes	—
379	#95	C₂×C₄×C₁₂₇	1	2	yes	—
380	#95	C₂×C₄×C₁₂₇	1	2	yes	—
381	C₂⁴	C₂²×C₄×C₁₂₇	1	2	yes	—
382	C₂⁴	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	C₂×C₈×C₁₂₇	1	8	yes	complemented
388	C₂×D₄	C₂×C₈×C₁₂₇	1	4	yes	complemented
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	C₂×C₈×C₁₂₇	1	4	yes	complemented
405	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
406	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
407	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
408	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
410	C₂²×C₄	C₂²×C₄×C₁₂₇	1	2	yes	—
411	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
412	C₂²×C₄	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₂₇	1	2	yes	—
414	C₂²×C₄	#41×C₁₂₇	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₂₇	1	1	yes	characteristic
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	8	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	4	8	no	—
431	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
432	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
433	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
434	C₂×C₈	C₂×D₄×C₁₂₇	1	2	yes	—
435	C₂×C₈	#41×C₁₂₇	1	2	yes	—
436	C₂×C₈	#41×C₁₂₇	1	2	yes	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	C₂×C₈×C₁₂₇	1	4	yes	complemented
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	C₂×C₈×C₁₂₇	1	8	yes	complemented
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×D₄×C₁₂₇	1	2	yes	—
453	C₄²	#41×C₁₂₇	1	2	yes	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	C₄×D₄×C₁₂₇	1	2	yes	—
465	C₂³	C₂²×C₈×C₁₂₇	1	4	yes	—
466	C₂³	C₂²×C₈×C₁₂₇	1	2	yes	—
467	C₂³	#131×C₁₂₇	1	2	yes	—
468	C₂³	C₂³×C₄×C₁₂₇	1	1	yes	characteristic
469	D₄	—	2	16	no	—
470	D₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
498	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
499	C₂×C₄	C₄×D₄×C₁₂₇	1	2	yes	—
500	C₂×C₄	C₂²×C₈×C₁₂₇	1	2	yes	—
501	C₂×C₄	C₂²×C₈×C₁₂₇	1	4	yes	—
502	C₂×C₄	C₂²×C₈×C₁₂₇	1	2	yes	—
503	C₂×C₄	#131×C₁₂₇	1	2	yes	—
504	C₂×C₄	#131×C₁₂₇	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₂₇	1	1	yes	characteristic
507	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
510	C₂×C₄	C₂×#41×C₁₂₇	1	1	yes	characteristic
511	C₈	—	2	2	no	—
512	C₈	—	2	2	no	—
513	C₈	—	2	2	no	—
514	C₈	—	4	2	no	—
515	C₈	—	4	2	no	—
516	C₈	#121×C₁₂₇	1	4	yes	direct product factor
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	C₈×D₄×C₁₂₇	1	4	yes	complemented
531	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
532	C₂²	C₂×C₄×D₄×C₁₂₇	1	1	yes	characteristic
533	C₂²	C₄×#41×C₁₂₇	1	1	yes	characteristic
534	C₂²	C₂³×C₈×C₁₂₇	1	1	yes	characteristic
535	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
536	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
537	C₂²	C₂×#131×C₁₂₇	1	1	yes	characteristic
538	C₄	—	2	2	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	C₈×D₄×C₁₂₇	1	4	yes	complemented
546	C₄	C₂×#121×C₁₂₇	1	1	yes	characteristic
547	C₄	#525×C₁₂₇	1	1	yes	characteristic
548	C₄	#529×C₁₂₇	1	1	yes	characteristic
549	C₄	#532×C₁₂₇	1	1	yes	characteristic
550	C₂	—	2	4	no	—
551	C₂	—	4	4	no	—
552	C₂	C₄×#121×C₁₂₇	1	1	yes	characteristic
553	C₂	C₂×C₈×D₄×C₁₂₇	1	1	yes	characteristic
554	C₂	C₂×C₈×D₄×C₁₂₇	1	1	yes	characteristic
555	C₂	C₁₂₇×#2929	1	1	yes	characteristic
556	C₂	C₁₂₇×#2931	1	1	yes	characteristic
557	C₂	C₈×#41×C₁₂₇	1	1	yes	characteristic
558	C₂	C₁₂₇×#2966	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₁₂₇	C₂³
commutator	C₂²	C₂³×C₈×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₂₇
socle	C₂³×C₁₂₇	C₂³×C₄
prime radical	C₂×#121×C₁₂₇	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₂₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₈×D₄×C₁₂₇	C₂	semidirect
2. C₂×C₈×D₄×C₁₂₇	C₂	semidirect
3. C₂²×C₄×C₈×C₁₂₇	C₂	semidirect
5. C₁₂₇×#1954	C₂	semidirect
6. C₁₂₇×#1939	C₂	semidirect
7. C₁₂₇×#1923	C₂	semidirect
8. C₁₂₇×#1869	C₂	semidirect
9. C₁₂₇×#1797	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₂₇	C₂	semidirect
11. C₈×C₂²⋊C₄×C₁₂₇	C₂	semidirect
58. C₂²×C₈×C₁₂₇	D₄	semidirect
65. #121×C₁₂₇	C₈	direct (N × H)
97. C₄×C₈×C₁₂₇	D₄	semidirect
107. C₂×D₄×C₁₂₇	C₂×C₈	semidirect
108. C₂×D₄×C₁₂₇	C₂×C₈	semidirect
124. C₂²×C₄×C₁₂₇	C₂×C₈	semidirect
160. C₄⋊C₄×C₁₂₇	C₂×C₈	semidirect
165. C₂²⋊C₄×C₁₂₇	C₂×C₈	semidirect
236. C₈×C₁₂₇	#121	direct (N × H)
250. C₂²×C₁₂₇	C₈×D₄	semidirect
265. C₄×C₁₂₇	C₈×D₄	semidirect
270. C₈×#121	C₁₂₇	direct (N × H)
280. C₂×C₈×D₄	C₂×C₁₂₇	semidirect
281. C₂×C₈×D₄	C₂×C₁₂₇	semidirect
282. C₂²×C₄×C₈	C₂×C₁₂₇	semidirect
284. #1954	C₂×C₁₂₇	semidirect
285. #1939	C₂×C₁₂₇	semidirect
286. #1923	C₂×C₁₂₇	semidirect
287. #1869	C₂×C₁₂₇	semidirect
288. #1797	C₂×C₁₂₇	semidirect
289. C₈×C₄⋊C₄	C₂×C₁₂₇	semidirect
290. C₈×C₂²⋊C₄	C₂×C₁₂₇	semidirect
291. C₁₂₇	C₈×#121	direct (N × H)
338. C₂²×C₈	D₄×C₁₂₇	semidirect
345. #121	C₈×C₁₂₇	direct (N × H)
377. C₄×C₈	D₄×C₁₂₇	semidirect
387. C₂×D₄	C₂×C₈×C₁₂₇	semidirect
388. C₂×D₄	C₂×C₈×C₁₂₇	semidirect
404. C₂²×C₄	C₂×C₈×C₁₂₇	semidirect
440. C₄⋊C₄	C₂×C₈×C₁₂₇	semidirect
445. C₂²⋊C₄	C₂×C₈×C₁₂₇	semidirect
516. C₈	#121×C₁₂₇	direct (N × H)
530. C₂²	C₈×D₄×C₁₂₇	semidirect
545. C₄	C₈×D₄×C₁₂₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₈×D₄×C₁₂₇	2
C₂²×C₄×C₈×C₁₂₇	2
C₄×#121×C₁₂₇	2
C₁₂₇×#1954	2
C₁₂₇×#1939	2
C₁₂₇×#1923	2
C₁₂₇×#1869	2
C₁₂₇×#1797	2
C₈×C₄⋊C₄×C₁₂₇	2
C₈×C₂²⋊C₄×C₁₂₇	2
C₈×#121	127

Subgroups — C8×#121×C127 #44585158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#121×C₁₂₇ #44585158